Many residents in the Rockaways neighbourhood of New York are entering their third week without power. Photograph: John Minchillo/AP

New York officials are set to ask for more than $30bn in federal disaster aid to help recover from superstorm Sandy as power firms prepare to hook up the last remaining homes still without electricity.

The state-owned Long Island Power Authority (Lipa) said it expected to restore power to most of the remaining 75,000 homes and businesses by the end of Tuesday – two weeks after the hurricane battered the region.

Other utility firms in the region – ConEd in New York and units of Public Service Enterprise Group Inc and FirstEnergy Corp in New Jersey – restored service to almost all customers over the weekend.

In all, Sandy left some 8.5 million electric customers without service in 21 states.

The storm hit Lipa harder than any other power company, knocking out more than 1 million of its 1.1 million customers.

Adding to its woes, a nor'easter last week knocked out power to 123,000 more customers, many of whom had had only just had their power restored after Sandy.

Power firms said reconnecting cut off customers back to the grid proved to be the biggest challenge they have faced.

But for many, the response by the utilities firms was not good enough. Lipa itself has said it is still unable to reconnect thousands of homes and businesses in the Rockaways due to flood damage making it difficult to repair electric cables.

New York governor Andrew Cuomo has repeatedly attacked all of the affected New York power companies.

"I share New Yorkers' frustration, I understand, we are not happy with the preparations or rate of recovery from the utilities companies. I promise the people of this state that utilities companies will be held accountable," the governor said last week.

Cuomo is now spearheading the state's case for billions of dollars in federal assistance, according to a report Monday in the New York Times.

The newspaper states that the governor's advisory panel have provided a staggering inventory of repair needs.

Included is a requirement for $3.5bn to fix damaged bridges, $1.65bn to rebuild homes and $1bn to reimburse emergency services and city officials for overtime.

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